Calibration Weights

Another important application is for the determination of formula weights. Calibration curves of log(formula weight) versus Vj are prepared between the exclusion limit and inclusion limit (figure 12.36). Since the retention volume is, to some... 

Linear type columns are especially designed to have wider linear molecular weight ranges. These linear-type columns are highly recommended for correcting nonlinear sections of molecular weight calibration curves (Table 6.2). 

Quality assurance for size exclusion supports is based primarily on the reproducibility of molecular weight calibrations. Although the reproducibility of the exclusion and inclusion limits is important, the distribution coefficients (Ko) of included standards are a better indication of duplication. Table 10.3 (page 314) shows such data for the SynChropak GPC and CATSEC supports. 

Molecular weight calibration from a monomer to several million daltons can be carried out by a variety of techniques. Because narrow standards of p(methyl methacrylate) (pMMA) are available, these are often used. Narrow standards of p(styrene) (pSty) are also available and can be used. Using the Mark-Houwink-Sakurada equation and the parameters for pSty and pMMA, a system calibrated with pSty can give pMMA-equivalent values, and vice versa. 

Herein are reported improved methods of molecular weight calibration where simultaneously, peak broadening parameters (a) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight calibration curve obtained using narrow MWD polystyrene standards. 

The second method assumes that the molecular weight calibration curve is linear on a semilog plot and should be employed where universal calibration is not practical as with aqueous SEC. Several variants of these methods involving different molecular weight data for the standards are discussed. The proposed methods have been evaluated using aqueous SEC and polydextran standards and nonaqueous SEC with polyvinylchloride standards. 

Previous methods of molecular weight calibration using broad MWD standards were of three basic types. Those which employ a broad MWD standard with known molecular weight distribution... 

Those which employ one or more broad MWD standards with known M or [n] and assume a linear molecular weight calibration curve and finally those which employ one broad MWD... 

Mjj and My or [q] for the broad MWD standard are taken as known quantities. Fy(v) is the normalized chromatogram for the broad MWD standard obtained with a mass detector. D2 is the slope of the molecular weight calibration curve at the peak position of the chromatogram (the equation of the tangent is given by M(v) = Dj exp(-D2v). is the variance of the single-species chromatogram... 

Methods Based on Universal Molecular Weight Calibration Curve... 

The nonlinear universal molecular weight calibration curve may be expressed as shown in equation ( ). 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

Methods which assume a linear molecular weight calibration curve will now be briefly considered. 

The assumed form of the linear molecular weight calibration curve is given in equation (lO)... 

Methods based on universal calibration will be illustrated using nonaqueous SEC and broad MWD PVC standards. The and of these standards is known. Methods based on the linear molecular weight calibration will be illustrated using aqueous SEC and broad MTO polydextran standards for which M and My are known. 

Figure L Molecular weight calibration curve for polystyrene an universal molecular weight calibration curve based on polystyrene ((%) [rj]Mw (U) w)...

The molecular weight calibration curves obtained for PVC are shown plotted in Figure 3. Table III shows an investigation of the effect of the peak broadening parameter (a) assumed when a single broad MWD PVC standard is used. The corrections for imperfect resolution for PV2 and PVC with a a = 0.5 are now reduced to about k% for both standards. It is of interest to note that with a reduced correction for imperfect resolution the Mark-Houwink exponent obtained is closer to published literature values for PVC in THF (13). The use of the associated molecular weight calibration curve for PVC would reproduce the M j and M of the PVC standards with errors of about 15. ... 

Figure 3. Molecular weight calibration curves for polyvinyl chloride obtained using universal calibration and one and two broad MWD standards (two broad standard method (0) [rj = 7.06 X 10 single broad standard method ...

We now move on to aqueous SEC and the use of the method of calibration based on a linear molecular weight calibration curve and two broad MWD polydext ran s with known and M. ... 

Figure 4. Molecular weight calibration curves for polydextran obtaimd u g linear calibration and two broad M WD standards and by plotting Mrm ( / Mif Mw) vs, peak retention volume ((%) Mrms, (---------) M(v) = 0,37 X exp(—OJ v))...

Two improved methods of molecular weight calibration using broad MWD standards have been proposed and some evaluation has been done experimentally for aqueous and nonaqueous SEC. The experimental evaluations indicate that both methods appear very promising and justify further experimental investigation. It is recommended that these new calibration methods be evaluated for a wide range of polymers,packings and mobile phases. 

This behavior shows that the dimensions of these polymers are independent of pH, ionic strength (in the ranges studied) and presence or absence of Tergitol or polyethyleneoxide. This result is of considerable help in interpretation of GPC behavior since in the absence of polymer-glass substrate interactions, the molecular weight calibration curves (log MW vs. elution volume) should be independent of pH, ionic strength or the two nonionic surfactants investigated. 

Figure 2. Molecular weight calibration curves for nonionic polyacrylamide for a single column (4 ft X Vs in. i.d.) containing 2000 A CPG-10 (200/400 mesh) packing with aqueous salt solutions as mobile phase.

Figure 7. Molecular weight calibration curve for nonionic polyacrylamides for a 6-column combination (each 4 ft X in, Ld.) with 3000 A, 3000 A, 2000 A, 1000 A, 729 A, and 500 A CPG-10 (200/400 mesh) packing.

Number and weight average molecular weights for Polysciences Standards and McMaster Standard B, calculated from raw chromatograms using the molecular weight calibration curve M(V) = 0.20 X 10 exp(-0.341 V - 0.006 V ) with V in counts (1 count = 5 ml). 2... 

P = exp(-(D2a) /2) with D2 the slope of the molecular weight calibration curve at the peak position of the chromatogram of the Standard. 

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